Choquet Expected Utility Model Research Articles

A Revealed Preference Test for Choquet and Max-Min Expected Utility with Ambiguity Aversion

We develop a revealed preference test for the Choquet expected utility model with ambiguity aversion, which does not rely on specific functional form assumptions on the utility index. It is computationally efficient if the number of states is not too large, even for a large number of observations. This is a nice feature compared to other existing revealed preference tests for decision models with ambiguity. We illustrate the usefulness of our results by implementing our test on two experimental datasets from the literature, and we compare the empirical fit of this model to the subjective expected utility model. (JEL C91, D81, D91, G41)

Optimal Risk Sharing for Maxmin Choquet Expected Utility Model

Optimal Risk Sharing for Maxmin Choquet Expected Utility Model

Separate aggregation of beliefs and values under ambiguity

Maximin expected utility model for individual decision making under ambiguity prescribes that the individual posits independently a utility function and a set of probability distributions over events to represent the values and belief, respectively. It assumes that individual evaluates each act on the basis of its minimum expected utility over this class of distributions. In this paper, we attempt to generalize the model to social decision making. It is assumed that the society’s belief is formed through a linear aggregation of individual beliefs and society’s values through a linear aggregation of individual values. We propose principles which characterize such separate aggregation procedures. We also generalize Choquet expected utility model, which posits a nonadditive measure over events and a utility function to represent belief and values, respectively. We prove that the only aggregation procedures that respect our principles are the separate linear aggregations of beliefs and values

Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty

We provide possibility results on the aggregation of beliefs and tastes for Monotone, Bernoullian and Archimedian preferences of Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci, and Siniscalchi (2011). We propose a new axiom, Unambiguous Pareto Dominance, which requires that if the unambiguous part of individuals’ preferences over a pair of acts agree, then society should follow them. We characterize the resulting social preferences and show that it is enough that individuals share a prior to allow non dictatorial aggregation. A further weakening of this axiom on common-taste acts, where cardinal preferences are identical, is also characterized. It gives rise to a set of relevant priors at the social level that can be any subset of the convex hull of the individuals’ sets of relevant priors. We then apply these general results to the Maxmin Expected Utility model, the Choquet Expected Utility model and the Smooth Ambiguity model. We end with a characterization of the aggregation of ambiguity attitudes.

THE RE-OPENING OF DUBINS AND SAVAGE CASINO IN THE ERA OF DIVERSIFICATION

In Dynamic Programing, mixed strategies consist of randomizing the choice of actions. In some problems, such as portfolio management, it makes sense to diversify actions rather than choosing among them purely or randomly. Optimal betting in casinos and roulette by a gambler with fixed goal was studied by Dubins and Savage [9] and their school without the element of diversification (betting simultaneously on different holes of the roulette), once it was proved (Smith's theorem - Smith [16], Dubins [8] and Gilat and Weiss [10]) that diversification does not increase the probability of reaching the goal. We question the scope of this finding, that was based on the assumption that the holes on which gamblers can bet are disjoint, such as 1 and BLACK in regular roulette. A counter example is provided in which holes are nested, such as 1 and RED. Thus, it may be rational for gamblers with a fixed goal to place chips on more than one hole at the table.This note is related to a joint work with Michèle Cohen on the preference for safety in the Choquet Expected Utility model.

The price for information about probabilities and its relation with risk and ambiguity

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker’s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.

Correlated equilibrium under uncertainty

We study strategic games in which each player lacks perfect understanding of opponents’ information structures, and as a result, does not know precisely the probability distribution governing opponents’ action choices. The Ellsberg Paradox demonstrates that when people act on unknown probabilities, their behavior may be inconsistent with the expected utility model. Motivated by the Ellsberg Paradox and related experimental findings, we assume that players’ preferences conform to the Choquet expected utility model of Schmeidler [Econometrica 57 (1989) 571] and the multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics 18 (1989) 141]. A generalization of correlated equilibrium is proposed.

Subjective ambiguity, expected utility and Choquet expected utility

Using the Savage set up, this paper provides a simple axiomatization of the Choquet Expected Utility model where the capacity is an inner measure. Two attractive features of the model are its specificity and the transparency of its axioms. The key axiom states that the decision-maker uses unambiguous acts to approximate ambiguous ones. In addition, the notion of ‘ambiguity’ is subjective and derived from preferences.

Diversification, convex preferences and non-empty core in the Choquet expected utility model

We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely “sure diversification.” We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index.

Sharing beliefs and the absence of betting in the Choquet expected utility model

Choquet expected utility maximizers tend to behave in a more “cautious” way than Bayesian agents, i.e. expected utility maximizers. We illustrate this phenomenon in the particular case of betting behavior. Specifically, consider agents who are Choquet expected utility maximizers. Then, if the economy is large, Pareto optimal allocations provide full insurance if and only if the agents share at least one prior, i.e., if the intersection of the core of the capacities representing their beliefs is non empty. In the expected utility case, this is true only if they have a common prior.

Uncertainty with partial information on the possibility of the events

The Choquet expected utility model deals with nonadditive probabilities (or capacities). Their dependence on the information the decision-maker has about the possibility of the events is taken into account. Two kinds of information are examined: interval information (for instance, the percentage of white balls in an urn is between 60% and 100%) and comparative information (for instance, the information that there are more white balls than black ones). Some implications are shown with regard to the core of the capacity and to two additive measures which can be derived from capacities: the Shapley value and the nucleolus. Interval information bounds prove to be satisfied by all probabilities in the core, but they are not necessarily satisfied by the nucleolus (when the core is empty) and the Shapley value. We must introduce the constrained nucleolus in order for these bounds to be satisfied, while the Shapley value does not seem to be adjustable. On the contrary, comparative information inequalities prove to be not necessarily satisfied by all probabilities in the core and we must introduce the constrained core in order for these inequalities be satisfied. However, both the nucleolus and the Shapley value satisfy the comparative information inequalities, and the Shapley value does it more strictly than the nucleolus.

Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences

This article deals with demand for insurance with a background risk in a nonprobabilized uncertainty framework, where preferences are represented by a nonadditive model of decision making. The Choquet expected utility model that we use generalizes expected utility and allows for a separation of the attitude towards uncertainty and the attitude towards wealth. When the insurable and the background risk are comonotone, the impact of the background risk on the demand for insurance is related to the attitude towards wealth. In contrast, when the two risks are anticomonotone, the attitude towards uncertainty is determinant. In this case, some of the resulting behaviors cannot be explained by the standard expected utility model.

Least convex capacities

Debreu proposed the notion of `least concave utility' as a way to disentangle risk attitudes from the certainty preferences embedded in a von-Neumann Morgenstern index. This paper studies preferences under uncertainty, as opposed to risk, and examines a corresponding decomposition of preference. The analysis is carried out within the Choquet expected utility model of preference and is centered on the notion of a least convex capacity.

An experiment on the evaluation of information under risk and ambiguity

Assume a decision maker has a choice between several acts. Some of the alternatives are simple lotteries; others consist of gathering additional (costy) information on outcomes or probabilities of the available simple lotteries prior to making a binding choice between them. In this paper hypotheses are derived from the Choquet Expected Utility model about the relationship between the degree of ambiguity aversion and the willingness-to-pay for information revealing the outcome of simple two-state-lotteries. These hypotheses are tested experimentally. 157 students are asked to state their willingness-to-pay for information, revealing the true payment relevant state, before making choices between a certain amount of money and two-state-lotteries of varying degrees of ambiguity. In the experiment the pessimism predicted by the Choquet Expected Utility model is not observed empirically.